The hook of a known play-free hook-type connection of the described kind (German Gebrauchsmuster No. 1,923,535) is formed by a flexible shank which comprises, near its end which is remote from the first part, a protrusion which extends transversely of the longitudinal direction of the shank. This protrusion comprises a pressure edge which is situated in the bending plane of the shank and which encloses an acute angle with respect to a plane extending transversely of the longitudinal direction of the shank. If a sufficiently high self-tightening effect is to be ensured in such a known hook-type connection, a comparatively rigid hook is chosen and/or comparatively small angle is chosen between the pressure edge and the said plane extending transversely of the longitudinal direction of the shank. These two steps separately as well as the two steps combined lead to a substantial restriction of the freedom of design, notably as regards the dimensions of the relevant parts and the hook-type connection between these parts.